Mechanics dictate where and how freshwater fission

Paul T. Malinowskia,1, Olivier Cochet-Escartina,1, Kelson J. Kaja, Edward Ronana, Alexander Groismana, Patrick H. Diamonda, and Eva-Maria S. Collinsa,b,2

aPhysics Department, University of California, San Diego, La Jolla, CA 92093; and bDivision of Cell & Developmental Biology, University of California, San Diego, La Jolla, CA 92093

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved August 28, 2017 (received for review January 17, 2017) Asexual freshwater planarians reproduce by tearing themselves body axis a divides affects the fitness and reproductive into two pieces by a process called binary fission. The resulting behaviors of its offspring (7, 11–13), understanding how fission head and tail pieces regenerate within about a week, forming two location is regulated is an important question to be answered. new worms. Understanding this process of ripping oneself into Regarding the division process, Vandel described fission as a two parts poses a challenging biomechanical problem. Because mechanical process, whereby the anterior and posterior parts act planarians stop “doing it” at the slightest disturbance, this independently, with the anterior part rhythmically pulsing and remained a centuries-old puzzle. We focus on japonica the posterior part largely adhering to the substrate. fission and show that it proceeds in three stages: a local constric- Here we focus on the biomechanics of fission in the asexual tion (“waist formation”), pulsation—which increases waist longi- planarian Dugesia japonica. Using time-lapse video recording, tudinal stresses—and transverse rupture. We developed a linear statistical analysis, and mathematical modeling, we show that mechanical model with a planarian represented by a thin shell. The Vandel was right in interpreting fission as a mechanical process, model fully captures the pulsation dynamics leading to rupture but wrong in declaring the fission location unpredictable. We and reproduces empirical time scales and stresses. It asserts that dealt with the experimental challenges elaborated on above by fission execution is a mechanical process. Furthermore, we show decapitating specimens to increase fission frequency and re- that the location of waist formation, and thus fission, is deter-

cording events over the course of months to obtain data of the BIOPHYSICS AND mined by physical constraints. Together, our results demonstrate necessary quality for quantitative shape analysis. These imaging COMPUTATIONAL BIOLOGY that where and how a planarian rips itself apart during asexual data were complemented by traction force experiments using reproduction can be fully explained through biomechanics. special substrates, which were sufficiently soft and stable to allow for these kinds of long-term experiments. planarians | biomechanics | fission | rupture | traction forces The analysis of 22 fissions made it possible to identify three key stages shared among all events we observed in this : a

ichael Faraday and his contemporaries were intrigued by local constriction (“waist formation”), pulsation—which increases PHYSICS Mthe observation that asexual freshwater planarians, squishy waist longitudinal stresses—and transverse rupture. As soft-bodied worms a few millimeters in length, reproduced by tearing , planarians exhibit these body shape changes through the themselves into a head and tail offspring, in a process called action of perpendicularly oriented, antagonistic muscle groups binary fission (1). How was it possible for these animals to on weakly compressible internal fluids and tissues, which make generate the forces necessary to rip themselves using only their up what is called a hydrostatic skeleton (see reviews in refs. 14 own musculature and substrate traction? The question has and 15). Waist formation is key to successful rupture, because it remained unanswered to this day, because it is experimentally difficult to study the fission process in sufficient detail to figure Significance out how it works. Planarian fission is fast, violent, and irregular. No induction mechanism has been identified, although de- capitation has been shown to increase fission probability (2–4). How planarians reproduce by ripping themselves into a head Furthermore, planarians are photophobic (5), fission occurs and a tail piece, which subsequently regenerate into two new primarily in the dark (4, 6), and even slight disturbances cause it worms, is a centuries-old biomechanics problem. Michael Far- to stop, complicating real-time imaging of the process. Finally, in aday contemplated how this feat can be achieved in the 1800s, the planarian species most commonly used in stem cell research, but it remained unanswered because it is experimentally dif- “ ” fission occurs on average approximately once per month per ficult to observe planarians doing it. We recorded Dugesia worm (7) and only lasts from a few minutes to tens of minutes japonica planarians in the act and developed a physical model (this study). All these factors make fission dynamics hard to that captures pivotal steps of their reproduction dynamics. The study and rendered it a neglected area of planarian research (8, model reproduces experimental time scales and rupture 9), although fission and regeneration are intimately linked (2, 3). stresses without fit parameters. The key to rupture is a local reduction of the ’s cross-sectional area, which greatly The most comprehensive study of fission that we have found in ’ the literature is the 1922 thesis (in French) of Vandel on asexual amplifies the stresses exerted by the planarian s musculature reproduction of several European Dugesia species (10). Vandel and enables rupture at substrate stresses in the pascal range. described fission as spontaneous and fast, varying in duration Author contributions: P.H.D. and E.-M.S.C. designed research; P.T.M., O.C.-E., and K.J.K. from seconds to minutes, and regulated but not triggered by performed research; E.R. and A.G. contributed new reagents/analytic tools; P.T.M., environmental factors. He noted that the fission plane is highly O.C.-E., and K.J.K. analyzed data; and P.T.M., O.C.-E., K.J.K., A.G., P.H.D., and E.-M.S.C. variable along the head–tail axis. Furthermore, by observing two wrote the paper. consecutive fissions of the same animal, the first occurring close The authors declare no conflict of interest. to the head and the second almost at the center, Vandel con- This article is a PNAS Direct Submission. cluded that it was “impossible to formulate rigorous conclusions. 1P.T.M. and O.C-E. contributed equally to this work. One must limit oneself to giving the general trends and looks of 2To whom correspondence should be addressed. Email: [email protected]. this phenomenon without trying to explain all the observed ex- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. ceptions” [author translation] (10). Because where along the 1073/pnas.1700762114/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1700762114 PNAS Early Edition | 1of6 Downloaded by guest on September 30, 2021 enhances the longitudinal stresses at a given longitudinal tension Methods) from the substrate (Fig. 1C), and “flesh waves,” axially force exerted by the planarian’s musculature by an order of propagating lateral indentations of the worm head, are produced magnitude. by contractions of circular muscle fibers. It appears that the We found fission to be distinctively different from the three generation of these waves is facilitated by the lack of contact known gaits of planarian locomotion, which are gliding, peri- (and, hence, of friction) between the lifted head and the sub- stalsis, and scrunching (16). Thus, fission poses a novel bio- strate. As the planarian body is nearly incompressible (hydro- mechanics scenario and the existing models that describe these static skeleton), these radial contractions produce longitudinal planarian gaits are inadequate to describe fission dynamics. head extension and stresses in the waist. To return to its original Following D’Arcy W. Thompson’sthesisthat“in the representa- shape the planarian then contracts its longitudinal muscles. tion of form and in the comparisons of kindred forms ... we discern Stresses in the waist are largest during the relaxation phase (con- the magnitude and the direction of the forces which have sufficed to traction) of the head. When the longitudinal stress in the waist convert the one form into the other” (17), we used the analysis of exceeds a critical value, rupture occurs (Fig. 1D) and the worm planarian body shapes to develop an enhanced readability thin- flesh rips into head and tail pieces, concluding the fission. The two cylindrical-shell model, which fully captures pulsation dynamics offspring regenerate into whole planarians in roughly a week. leading to rupture and reproduces empirical time scales and stresses. As the cartoon (Fig. 1) illustrates, fission dynamics are fairly Importantly, the model only uses experimental data and parameters complex. We first discuss where the waist forms. Then, we show from the literature as inputs. This implies that rupture is a purely how body shape analysis allows construction of a simple physical mechanical process that can be fully accounted for by physical model that explains how pulsation can lead to rupture and es- mechanisms without requiring any additional biological explanations. timate the magnitude of the rupture stresses. Besides solving this centuries-old mystery about the biomechanics of planarian reproduction, this study highlights the power of a prac- Location of Waist Formation. Vandel (10) observed that an indi- vidual planarian divided at different locations when followed tical approach, combining quantitative image analysis and a simple through consecutive fissions, which led him to the conclusion physical model, for gaining insights into a complex biological that the fission plane cannot be predicted. Because he did not phenomenon which is not accessible to controlled experimentation study D. japonica, we checked whether this observation held and perturbations. equally true in this species. Indeed, as illustrated by the examples Results in Fig. 2A, the fission location varies and it is seemingly impos- sible to predict where an individual planarian fissions (note that Months of continuous recording of decapitated D. japonica the dynamics of these fission events were not recorded). allowed us to capture a sufficient number of fission events oc- We then took advantage of a unique large-scale dataset on the curring in open space for a quantitative study of fission dynamics. – birth and division sizes, growth curves, and time between fis- Decapitation promotes fission (2 4) without altering its dy- sions (reproductive waiting time, RWT) we had accumulated on namics (Movies S1 and S2) and was thus used as a means to D. japonica (18) and applied statistical analysis to assay whether increase the number of events. Qualitative analysis of these time- those data would provide further insight. We found an asym- lapse movies indicated that D. japonica fission occurs as a se- metric double-Gaussian distribution for the waist location based quence of three distinct stages: waist formation, pulsation, and on imaging n = 1,335 specimens within 3 d after fission (Fig. 2B ’ rupture (Fig. 1 and Movie S2). Fission relies on the animal s thin and Materials and Methods). Of note, the area of low fission μ (10 m) subepidermal muscle network (14), which consists of probability between the peaks, as determined by manual in- – longitudinal (parallel to the head tail axis), circular (perpen- spection of a subpopulation of n = 40 specimens, coincides with – dicular to the head tail axis), and diagonal muscles (Fig. S1). the location of the pharynx, which is a powerful muscle used to ’ Given the muscles anatomical orientation, the vertico-lateral ingest food (19). Thus, planarians divide neither at a pole nor at narrowing which leads to the formation of a waist is mediated by the pharynx but have a nonzero probability of dividing anywhere local contractions of circular muscles. Narrowing causes the waist else along the head–tail axis, with the majority of events hap- region to lose contact with the substrate, while the body mass is pening posterior to the pharynx. This distribution of waist posi- actively redistributed toward the head and tail, leading to the for- tion also explains why planarian fission is generally reported in mation of broad regions of contact with the substrate (Fig. 1B). the literature as occurring posterior to the pharynx (20–22). Next, the pulsation stage starts, as the planarian lifts its head Whether a planarian divides pre- or postpharynx has a sig- (whenever we use the term “head,” we refer to the region an- nificant effect on its offspring, because it determines birth size terior to the waist. The true head was amputated in our exper- and thus offspring survival and reproductive success (7). We iments as indicated in Fig. 1A and described in Materials and therefore binarized the data in Fig. 2B into pre- (%H < 0.56) versus postpharynx (%H ≥ 0.56) fissions and correlated it with other known quantities about the properties and history of these worms. While the following arguments hold true for all D. japonica, we only discuss individuals originating from a head offspring below, because prepharynx fissions are negligible for planarians that originate from tails (<<1%). We found a strong correlation between a planarian’sRWTand fission location (Fig. 2C), whereas the planarian’s size at division had no effect (Fig. S2). Nearly all prepharynx fissions resulted from wormswithshortRWTs(<2wk;Fig.2C). Upon inspection of the physical characteristics of these planarians, we found that we can predict where (either pre- or postpharyngeally) an individual Fig. 1. Cartoon of D. japonica fission. (A) Unperturbed planarian before D. japonica will divide through quantification of its relative pharynx fission. The pharynx is marked by the blue arrowhead. To increase the fission position (Fig. 2D). Fission occurs anterior to the pharynx when rate (3), we amputate as indicated by the gray line. (B) Waist formation. Tissue movement causes local narrowing (orange arrowhead) and formation the pharynx is located relatively closer to the tail (Fig. 2D). This is of wide contact regions at the head and tail (green arrowheads). The waist is frequently the case for animals with short RWTs (Fig. S2). A not in contact with the surface. (C) The head lifts off the substrate during comparison of pharynx positions at birth and at division of pre- and pulsation and then readheres and slides back against the surface. (D) Rupture. postpharyngeal dividers shows that the former have not repositioned

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1700762114 Malinowski et al. Downloaded by guest on September 30, 2021 AB formation is critical for successful fission. It has the physiological benefit of preventing gut spillage during the subsequent rupture. Not less importantly, for a given longitudinal tension force, the reduction in the worm cross-section in the waist region leads to a proportional amplification of the longitudinal tensile stress. That said, the waist diameter is anatomically constrained and scales with the initial width of the worm (Fig. S4 and SI Text). This scaling indicates the existence of a mechanism preventing the formation of waists that are too narrow. Experimentally, we found that the ratio of cross-sections of the head, Ahead, and of the waist, Awaist,is CD limited by ∼14, suggesting that the tensile stress at the waist can be amplified by a factor of up to ∼14, compared with the characteristic traction stress in the head (or the tail) (Fig. S4 and SI Text).

Pulsations. Once the waist is formed, pulsations begin, that is, the planarian executes multiple longitudinal extensions and contrac- tions of the head and/or tail parts of its body (Fig. 3 A–C, Fig. S3 C and D,andMovies S5 and S6). On average, head pulses occur more frequently than tail pulses (89 head pulses versus 19 tail pulses total for n = 22 fissions), suggesting that head pulses are EF critical for generating tensile stresses causing the rupture in the G waist region. Notably, head and tail pulses were asynchronous and we never observed a “tug-of-war” between them. At the beginning of each head pulse, the anterior of the head detaches from the substrate (Fig. 2G, Fig. S5,andMovies S4 and BIOPHYSICS AND

ACCOMPUTATIONAL BIOLOGY B Fig. 2. Waist formation. (A) The waist position along the head–tail axis is not conserved across generations for a single planarian line. (B) Frequency of occurrence of waist position, expressed as percentage head at division (n = 1,335). (C) Quantification of the fraction of prepharynx fissions as a function of RWT. (D) Quantification of percentage head at division as a function

of relative pharynx position shows that the latter predicts fission position. PHYSICS (E) Color-coded maps of worm footprint, showing a representative sequence DE of waist formation in an amputated planarian. Colors indicate the change in the mass per unit area, with green corresponding to no change, blue to loss, and red to gain of mass. (Scale bar: 1 mm.) (F) The width of the waist region versus time in E.(G) Side view image of a planarian undergoing fission. The dashed red line outlines the Petri dish wall. The white arrow highlights a gap between the waist of the worm and the substrate. The blue line indicates the angle by which the planarian lifts its head before pulsation. (Scale bar: 1 mm.)

their pharynx sufficiently to allow for a postpharyngeal fission. F Because repositioning takes time, this can explain why we primarily observe prepharynx divisions in rapid dividers. We can explain why pharynx position matters with bio- mechanical arguments. To pull itself apart, a planarian needs to G form two sufficiently large contact regions (adhesion patches) with the substrate. If the pharynx is located close to the tail end, the posterior part of the animal is too small to accommodate the adhesion patches and fission occurs anterior to the pharynx (Fig. S2). Because the size of these patches scales with worm size (Fig. S2), absolute worm size does not matter. To summarize, our statistical analysis shows that it is possible to predict whether a particular D. japonica planarian will fission pre- or postpharynx, solely through quantification of its relative pharynx position.

Mechanism of Waist Formation. Waist formation, which is a local Fig. 3. Pulsation. (A) Representative sequence of head pulsation of an am- narrowing in the vertical and lateral directions, is achieved by putated planarian. Color coding is the same as in Fig. 2. (Scale bar: 3 mm.) (B) contractions of circular muscles. Peristaltic contractions move Kymograph showing multiple head pulses. (Vertical scale bar: 20 s; horizontal mass from the waist region toward the head and tail (Fig. 2 E and scale bar: 1 mm.) (C). Head length as a function of time during a series of head pulsations. (D) Head extension is logistic and fast, whereas (E) head contraction F, Fig. S3 A and B, and Movie S3). As a result of this mass re- is linear and slow. (F and G) Head and waist lengths are anticorrelated. distribution, the area of contact with the substrate on either side (F) Consecutive images of a planarian with its head and waist lengths shown by of the waist increases, whereas the waist part of the worm body red and blue lines, respectively. (Scale bar: 3 mm.) (G) Time dependences of detaches from the substrate (Fig. 2G and Movie S4). Waist head length and waist length of the planarian from the images in F.

Malinowski et al. PNAS Early Edition | 3of6 Downloaded by guest on September 30, 2021 S7). The detachment allows the head to break out of the mucus ∼70-μm-thick surface layer as the tracer particles (SI Materials and layer (Figs. S5 and S6 and SI Text), minimizing friction with the Methods). A map of displacements of the beads from their zero- substrate during head extension. Circular muscle contractions then stress locations (when the substrate was not deformed by the elongate the head (Fig. 3D and Fig. S3). This is a necessity of the worm)wasgeneratedandconvertedintoamapoftractionstresses planarian’s hydrostatic skeleton: If a worm elongates, while both its using previously published algorithms (24) (SI Materials and width and height decrease, it can only be a result of contraction of Methods). The stresses were on the order of 100 Pa (Fig. 4B). the circular muscles. The head reattaches to the substrate and slowly Projection of the stresses on the axis of the worm (direction contracts. Head contraction is achieved by shortening of the worm’s along the waist) was then integrated over the areas of the head longitudinal muscles and resisted by friction with the substrate (Fig. and of the tail, providing the pair of opposing traction forces that 3E). These different dynamics are clearly seen in Fig. 3 D and E), stretch the waist. The stretching force before rupture was a few where head length during pulsation increases logistically (S shape hundred micronewtons and, when divided by the cross-sectional in Fig. 3D) but decreases linearly with time. Importantly, head and area of the waist, it provided an estimate of ∼2,000 Pa for the waist dynamics are anticorrelated. As the head extends, the waist tensile stress in the waist immediately before rupture. Once gets compressed and buckles (Movies S5 and S6). As the head rupture is completed, the two offspring move independently and contracts, the waist region gets stretched (Fig. 3 F and G). regenerate into new full worms within about a week. The maintenance of proper adhesion with the substrate is crucial A comparison of the fission dynamics of events on soft poly- during this stage. We observed some animals slipping during pul- dimethylsiloxane gels versus plastic Petri dishes revealed no sation (Fig. S6) and interpret this as resulting from weak adhesion significant differences in terms of the number of pulses (Fig. S6), with the substrate, leading to poor stress transmission to the waist. suggesting that the interaction with the mucus dominates sub- In accordance with this interpretation, animals that slip execute strate effects on fission. more pulsations before rupture. Interestingly, the number of pulses It is evident from this quantitative analysis that fission dynamics was weakly anticorrelated with a planarian’s size, suggesting that the have little in common with normal planarian locomotion via cilia- absolute size matters for successful fission (Fig. S6). In other situ- based gliding, which does not involve body shape changes (16). ations where substrate adhesion is critical, we and others have There are some similarities between fission and the two muscle- shown that an increase in mucus secretion is key (16, 23). To di- based planarian gaits, peristalsis and scrunching (16, 23), insofar rectly prove the link between a planarian’s mucus secretion and as all involve body elongation–contraction cycles and require good adhesion, we treated planarians with Triton X-100, which increased contact with the substrate for successful execution. However, fission mucus secretion (Fig. S6). Using a custom aspiration setup, we then pulsation dynamics are different from those observed in peristalsis quantified the aspiration force required to detach worms from their or scrunching, which either show no asymmetry or relatively longer substrate. Triton X-100–exposed planarians required larger aspira- elongation periods, respectively. Finally, waist formation is a unique tion forces than control planarians (Fig. S6). Based on these data, feature of fission. Because of these differences, existing models for we postulate that substrate adhesion during fission is mediated these gaits fail to reproduce the observed fission dynamics. through the increased presence of mucus. Therefore, we developed a linear mechanical model with the planarian head represented by a thin, cylindrical, elastic shell Rupture. The ultimate and key step in fission is successful rupture (corresponding to the thin musculature network) filled with a (Fig. 4A). Rupture occurs when the stress in the waist, induced by viscous liquid (corresponding to coarse-grained, squishy internal contraction of the head, exceeds a critical threshold (Fig. S4E). In tissue). The same model could be applied to the tail part on the most cases (20/22 fissions; Materials and Methods and Movie S8), other side of the waist, but we focus on the head because tail rupture is nucleated at the center of the waist region. We measured pulsations do not occur in all fission events. Although the de- the stresses exerted on the substrate during fission using trac- formations during fission are large, this linear thin-shell model tion force measurements (Fig. 4B). To this end, we fabricated allows us to capture pulsation and rupture dynamics using only thick (∼5 mm), soft (Young’s modulus E = 1.2 kPa) silicone gel physical arguments and scaling estimates. substrates with 30- to 45-μm-diameter beads imbedded in an Physical Model. We treat the head as a uniform, long, thin, cy- lindrical, elastic shell of cross-sectional radius R, Young’s mod- ulus E, and shell thickness h which encloses material of density ρ A (Fig. S1). Although planarians, being , have elliptical cross-sectional areas, the simplification to circular cross-sectional areas has a negligible effect on the results (SI Text). We assume that 0.00 s 18.4 21.0 the head is connected to the waist by an impermeable junction, through which no matter crosses on the time scale of pulsations B 2 Pa (Fig. S1). This assumption is reasonable, as the data show no ma- 140 terial transfer once the waist has been established (Movies S4 and 4 ∼ 120 S5). The long-thin approximation applies, since Lhead 4 mm while ∼ 6 Rhead 1.2 mm. 100 A thin, cylindrical, elastic shell supports three modes of waves: 8 80 longitudinal, flexural, and torsional. The last ones can be ignored as there is no indication that the planarian twists during pulsa- 10 60 tion. Longitudinal wave displacements on an elastic cylinder are 12 40 predominantly axial while flexural (F)-waves support primarily radial (lateral) displacements. These two modes are linearly 14 20 coupled at finite Poisson ratio (Eqs. S1–S3). The experimentally observed flesh waves correspond to F-waves. 5110 5 X-position (mm) They are initiated by contractions of circular muscles in the head part anterior to the substrate contact region, causing Fig. 4. Rupture. (A) Image sequence of a worm rupturing. (Scale bar: 2 mm.) local changes in the radius. The head anterior is detached from (B) Color-coded map of the substrate traction stresses produced by a D. japonica the substrate during extension and therefore has no friction with it. (contour in black) a short time before rupture. The deformation propagates longitudinally at the group velocity of

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1700762114 Malinowski et al. Downloaded by guest on September 30, 2021 F-waves. As the wave progresses anteriorly the head extends for- components by metalloproteinases, which have been shown to play ward due to volume conservation. Simultaneously, the wave prop- a role in planarian tissue homeostasis and regeneration) (29, 30). agates in the head posterior toward the waist region and because the To test whether such weakening of the fission zone was neces- head–waist connection is impermeable the waist region experiences sary, we measured the stresses needed to rip a nondividing pla- a compression and buckles. Thus, qualitatively, the model predicts narian apart by applying suction to both ends of a planarian using the observed anticorrelation of head and waist length during head pipette tips connected to a peristaltic pump (Fig. 5A and Materials extension. Furthermore, we can compare the F-wave group velocity and Methods). In this experiment (Fig. 5B), a waist was not formed with the observed flesh pulse speed (see SI Text for calculations). and the time to rupture was much shorter (seconds compared with Using only experimentally measured values of the parameters, we minutes in fission), rendering biochemically induced structural calculate that the F-wave propagates at vgv = 1.4 mm=s. This is in changes unlikely. However, this pulling experiment yielded stresses excellent agreement with the observed flesh pulse speed of comparable to those obtained in our traction force measurements, vext = 1.1 ± 0.4 mm=sðmean ± SE; n = 16Þ. Our model thus properly with values ranging between 7.0 kPa and 13.1 kPa. Additionally, we captures the dynamics of head extension during pulsations. quantified where the worms ruptured and contrasted these mea- Regarding the head contraction phase, the main difference to surements with the fission data (Fig. 5C). As expected, pulled extension is that the head anterior is now in contact with the planarians could tear anywhere along the head–tail axis, including substrate and thus friction needs to be taken into account. Head at locations which are “forbidden” zones in fission, such as the very contraction dynamics are determined by this competition be- anterior or posterior regions of the animal. tween muscular relaxation and friction with the substrate as in- We also estimated the stresses required to crush a planarian by ertial forces can be neglected. The balance of these two forces adding a small weight onto its trunk region (Fig. S5 and SI Text). defines a relaxation time scale (SI Text): Worms were crushed by a 5-g weight with a contact area of 2 σ = =  8.9 mm , thus exerting a stress of F/A 5.6 kPa. The results τ =~ η 2 [1] of these both tests indicate that stresses of a few kilopascals are relax mucus Acontact Lhead Vhead Ehmucus. sufficient to rupture a planarian. All values in Eq. 1 were experimentally determined, with Together, these data show that rupture during fission can be = μ η = · achieved through the planarian’s mechanical properties and the hmucus 10 m the height of the mucus layer, mucus 65 Pa s 2 the mucus viscosity, Acontact = 8.7 mm the surface area of contact physical mechanisms of pulsations and does not require enzymatic with the substrate, E = 500 Pa the elastic modulus of the shell, weakening. The planarian’s “trick” of progressive necking is key to 3 BIOPHYSICS AND Vhead = 22 mm the head volume, and Lhead = 4 mm the length of successful fission. Once rupture is initiated at these relatively low COMPUTATIONAL BIOLOGY the head (Table S1). Using these values gives τrelax =~ 82 s, which stresses of a few kilopascals, the cross-sectional area of the waist is in reasonable agreement with the experimental value of the decreases further and the internal stresses increase accordingly. We relaxation time τ = 44 ± 20 sðmean ± SE; n = 18Þ. found that the nerve cords break last during fission (Fig. S7). Be- Taken together, pulsation time scales are well captured by the cause their diameter is only 50 μm(Fig. S7), this implies stresses in linear model, both during elongation and contraction phases, al- the megapascal range, similar to what has been reported as the tensile strength limit for nerve tissues in other organisms (25, 31).

though it is too simple to reproduce the trajectory of pulsations PHYSICS (logistic during elongation and linear during contraction). Head extension is quick, whereas head contraction is slow and thus allows Discussion and Conclusions for the buildup of stresses in the waist required for rupture. The As an active, living biomaterial, D. japonica planarians are able to model correctly predicts that head extension and waist extension coordinate and execute their own dissection. Our results demon- are anticorrelated (Fig. S1), consistent with experimental obser- strate how they can develop sufficiently large tensile stresses to tear vations (Fig. 3 F and G). During head extension, the waist appears themselves apart. Because D. japonica are soft and squishy (32)— shorter, because it bends vertically (Fig. 3 F and G and Movies S4 with an elastic modulus 1,000 times smaller than that of nematodes and S5), whereas during head contraction the waist is extended (16, 33)—they are able to tear themselves apart using only substrate (Fig. 3 F and G) and thus under increased longitudinal stresses. adhesion and their own musculature. The self-inflicted rupture is Once these stresses exceed the tissue’s yield, rupture occurs. We facilitated by the formation of a narrow waist, where tensile stresses estimate this critical stress necessary for rupture (SI Text)usinga are amplified due to reduced cross-sectional area. Friction with the ’ linear approach and experimentally determined parameters only substrate, the mucus rheology, and the planarian s elastic modulus are key parameters in determining the dynamics of the contraction (Table S1) and obtain σwaist ≈ 3,000 Pa, which is in reasonable agreement with our traction force measurements. phase and, ultimately, rupture. The planarian only needs to exert

Magnitude of Rupture Stresses. The rupture stresses we found are in the kilopascal range, which is orders of magnitude lower than stresses previously reported for rupture of tissues in other animals A C 30 )

(25, 26). It is possible that biological processes preceding or ac- 2 25 companying waist formation weaken the waist and lower the re- B quired rupture stresses. The idea of a predefined “fission zone,” with 20 metabolic, cellular, or structural differences compared with the rest 15 of the worm, was already suggested over 50 years ago by Child (27) and Tokin (reviewed in refs. 2 and 28). Hori and Kishida (3) per- i 10 formed structural analysis of the postpharyngeal region and observed “ ” 5

presumptive changes in preparation for fissioning in some, but not area before rupture (mm all, of the samples. Because these samples were fixed planarians 0 without a waist, it is impossible to tell if fission would have occurred 010.2 0.4 0.6 0.8 ii in the studied region. Thus, experimental evidence demonstrating the % head after rupture existence of a fission zone is absent. Our data on the distribution of Fig. 5. Magnitude of rupture stresses. (A) Schematic of the planarian pull- the waist location argue against a permanent fission zone but allow ing experiment. (B) Representative image of a pulled planarian. (B, i) right for the possibility that the animal locally prepares for fission before before and (B, ii) right after rupture. (C) Distributions of rupture planes in each event (e.g., via enzymatic digestion of extracellular matrix fission (black circles, n = 22) and pulling (gray triangles, n = 16) experiments.

Malinowski et al. PNAS Early Edition | 5of6 Downloaded by guest on September 30, 2021 sufficiently large stresses to break the weakest structures. Once Materials and Methods tearing is initiated, the waist cross-sectional area decreases further Planarian Maintenance, Fission Experiments, and Analysis. Specimens of clonal and tensile stresses are greatly amplified, resulting in stresses able to asexual D. japonica were used for all fission experiments. Since planarians do break stronger anatomical features such as the muscles or nerve not need a brain to fission, specimens were decapitated to increase the cords. From a biomechanical standpoint one could argue that pla- likelihood of fission in the presence of light (34). Details on planarian narians fission because they are soft and thus can do it. However, maintenance, fission experiments, and analysis are provided in SI Materials that’s only one part of the story. Planarians fission because they and Methods. have stem cells which allow them to regenerate the missing struc- tures after the act. Fission is the sole mode of reproduction of the Single-Worm Statistical Data. Fissions were tracked using the SAPling data- asexual planarians studied here, which poses the question of how base and barcode system (35) and planarian head and tail sizes were this species creates population diversity. Where a planarian divides quantified as described in detail in SI Materials and Methods. affects the fitness and reproductive behaviors of its offspring (7, 11– Traction Force Measurements. Traction forces were measured using custom 13). Therefore, understanding how fission location is regulated is an gel substrates as described in detail in SI Materials and Methods. important evolutionary question to be answered. We showed that the waist and thus the fission location is de- Planarian Pulling. Planarians were subjected to external stresses using a termined through the relative position of the pharynx. Animals peristaltic pump (Cole Parmer). Upper and lower bounds for the stress applied with short RWTs have less time to reposition their pharynx fol- to the planarian were calculated using the peristaltic pump to lift chrome lowing the previous fission and thus mechanically cannot divide steel beads. Details are provided in SI Materials and Methods. postpharyngeally, frequently resulting in large tails. What causes some animals to divide rapidly, whereas other comparably sized ACKNOWLEDGMENTS. We thank the group of A. Ott for mucus rheology animals take a long time, remains unknown. However, now that experiments; R. Schwarz, J. Talbot, and B. Lincoln for help with fission we can predict where an individual will divide, we can start to dissect experiments; W. Shi for help with the drawings; and D. Kleinfeld, W. Kristan, whether molecular differences exist between pre- and postpharynx J. Posakony, M. Vergassola, and D. Hagstrom for discussions and comments on the manuscript. This work was supported by the Burroughs Wellcome dividers, which could provide insights into the mechanisms con- Fund Career Awards at the Scientific Interface and NSF CAREER Grant 1555109 trolling RWT and, if existent, a fission trigger. (to E.-M.S.C.), NSF Grant PHY 1205921 (to E.R. and A.G.), US Department of Finally, going beyond planarian reproduction, this study shows Energy Grant FG02-04ER54738 and the Center for Momentum Transport and how one can gain insights into complex animal behaviors that are Flow Organization (P.H.D.), and a Hellman undergraduate research scholarship difficult to access experimentally, simply by “watching.” Quanti- (to K.J.K.). The 6G10-C7 antibody developed by R. Zayas and the 3c11 antibody developed by E. Buchner were obtained from the Developmental Studies tative image analysis allows for the construction of simple physical Hybridoma Bank, created by the Eunice Kennedy Shriver National Institute of models which can then be tested against the empirical data, po- Child Health and Human Development of the NIH and maintained at the tentially revealing new regulatory mechanisms. Department of Biology, University of Iowa.

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